Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
Correct Answer
$6897
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5700 × 3% × 7
= $5700 ×3/100 × 7
= 5700 × 3 × 7/100
= 17100 × 7/100
= 119700/100
= $1197
Thus, Simple Interest = $1197
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1197
= $6897
Thus, Amount to be paid = $6897 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5700
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 7)
= $5700 + ($5700 ×3/100 × 7)
= $5700 + (5700 × 3 × 7/100)
= $5700 + (17100 × 7/100)
= $5700 + (119700/100)
= $5700 + $1197 = $6897
Thus, Amount (A) to be paid = $6897 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $171 × 7 = $1197
Thus, Simple Interest (SI) = $1197
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1197
= $6897
Thus, Amount to be paid = $6897 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(3) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(4) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
(9) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?